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Simulating diffusion processes in discontinuous media: benchmark tests. (English) Zbl 1349.65019
Summary: We present several benchmark tests for Monte Carlo methods simulating diffusion in one-dimensional discontinuous media. These benchmark tests aim at studying the potential bias of the schemes and their impact on the estimation of micro- or macroscopic quantities (repartition of masses, fluxes, mean residence time,\(\ldots\)). These benchmark tests are backed by a statistical analysis to filter out the bias from the unavoidable Monte Carlo error. We apply them on four different algorithms. The results of the numerical tests give a valuable insight into the fine behavior of these schemes, as well as rules to choose between them.

65C05 Monte Carlo methods
60J60 Diffusion processes
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